After takeoff, an airplane climbs at an angle of 30° at a speed of 215 ft/sec. how long does it take for the airplane to reach an altitude of 13,000 ft? (round your answer to one decimal place.)

120.9 seconds

Explanation:

*Attached below is a rough sketch of the problem. Point A represents the point where the airplane climbs 30°, BC represents the altitude of the airplane, AC represents the angular displacement of the airplane.

Parameters given:

Angle of elevation = 30°

Speed (angular) of the airplane = 215 ft/sec

Altitude = 13000 ft

We need to find the angular displacement of the airplane to find the time it takes to get to an altitude of 13000 ft. The angular displacement is represented by the hypotenuse of the triangle. Hence, using SOHCAHTOA,

∴ time taken =

Therefore, it will take the airplane 120.9 seconds to get to an altitude of 13000 ft.

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